Figures 3(a),(b) and (c) show the Co \(L_{2,3}\)  XAS and XMCD spectra of the same samples taken in the TFY mode. From the figure, it is clear that the XMCD intensities are much higher than those taken in the TEY mode. The large difference between the bulk-sensitive TFY mode with \(\sim \) 100 nm probing depth and the surface-sensitive TEY mode with \(\sim \) 5 nm probing depth suggests that there is a magnetically dead layer of \(\sim \) 5 nm thickness or more at the surface of the samples as in the case of rutile [1]}, [2]}. The presence of a surface dead layer of \(\sim \) 5 nm thickness is consistent with the recent measurements of the film-thickness dependence of AHE [3]}. The spectral line shapes of the XAS and XMCD spectra of all the samples taken in the TFY mode show broad features with spectral line shapes similar to those of rutile Co-doped TiO\(_2\)  [2]}. Both magnetization and XMCD intensity increased with carrier density. This is consistent with spin alignment arises due to the interaction of local spins with the spin polarized free carriers, in which carrier-mediated ferromagnetism and ferromagnetic ordering is realized. Yamada et al.[5]} have also demonstrated electrically induced ferromagnetism at room-temperature in anatase Ti\(_{1-x}\) Co\(_x\) O\(_{2-\delta }\) , by means of electric double layer gating resulting in high density electron accumulation (\(>\) 10\(^{14}\)  cm\(^{-2}\) ). By applying a gate voltage of a few volts, a low-carrier paramagnetic state was transformed to a high-carrier ferromagnetic state. This also supports theoretically as well as experimentally the idea that the ferromagnetism originates from a carrier-mediated mechanism [5]}, [7]}. The broadening of the TFY spectra may be due to the randomly displaced positions of Co atoms, which leads to in various local structures as suggested by the anomalous X-ray scattering study of Matsumura et al. [8]}. The experimental XAS and XMCD spectra are distinctly different from Co metal and show qualitatively good agreement with the calculated spectra for the Co\(^{2+}\)  in random crystal fields [9]}, where the calculations were done using the various electronic structure parameters as listed in Table I.
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